Question

An article considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi)....

An article considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = 1800 + 1.4x, and that the standard deviation of the random deviation ϵ is 350 psi.

(a) What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2000? (Round your answer to four decimal places.)

Answer: 0.1271

(b) What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2500? (Round your answer to four decimal places.)

Answer: 0.8051

(c)Consider making two independent observations on 28-day strength, the first for an accelerated strength of 2000 and the second for

x = 2500. What is the probability that the second observation will exceed the first by more than 1000 psi? (Round your answer to four decimal places.)

Answer: 0.2709

(d)Let Y1 and Y2 denote observations on 28-day strength when x = x1 and x = x2, respectively. By how much would x2 have to exceed x1 in order that P(Y2 > Y1) = 0.95? (Round your answer to two decimal places.

Answer: ????

Just need help on part D. All the other answers are correct.

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